Distributed tracking control for multiple Euler-Lagrange systems with communication delays and input saturation

Robust event-triggered cooperative control of uncertain multiple Euler-Lagrange systems based on three kinds of random transformation topologies

In this paper, we consider the consensus of uncertain multiple Euler-Lagrange​ systems. Based on switching topologies, the time-varying delay compensation, event-triggered mechanism, and finite-time convergence are considered, which can satisfy the needs of an actual system. First, the nonlinear uncertainties of the system are well approximated by applying the neural-networked scheme. Second, the new event-triggered mechanism can avoid the influence of the limited signal bandwidth and effectively decrease the data transmission times. Third, an adaptive law is used to compensate for the model and external disturbances. Fourth, the proposed switching topology scheme can respond to different scenarios, including when some agents fail to suddenly connect with their neighbors, and meet a wider range of collaborative needs. The effectiveness and feasibility of the proposed technique are demonstrated in theorem analysis and simulations.

FSG-based divinable time-varying formation tracking of multiple Lagrangian agents with unknown disturbances and directed graphs

In this paper, a flexible shape generator (FSG) is designed to achieve the divinable transformation process of the time-varying formation, and consider the FSG-based time-varying formation tracking (TVFT) problem of multiple Lagrangian agents with unknown disturbances and directed graphs. A hierarchical control algorithm is newly designed to achieve the control goal without using the prior information of the system model and bounded disturbances, and the specific implementation of the proposed hierarchical algorithms is also provided. By using the Hurwitz criterion and adaptive system theory, the sufficient conditions are derived and the stability analysis show that the formation tracking errors of the considered system are uniform ultimate bounded. Several simulation examples are performed on five two-degree-of-freedom mechanical arms to show the effectiveness of theoretical results.

Observer-based saturated proportional derivative control of perturbed second-order systems: Prescribed input and velocity constraints

This study introduces a new methodology for controlling second-order nonlinear systems in point-to-point tasks with simultaneous input and velocity saturation constraints. The proposed approach utilizes a robust disturbance observer for compensating for the unknown dynamics and disturbances affecting the system. Then, the disturbance observer is combined with a saturated proportional derivative (PD) controller. The resulting control signal allows solving the regulation problem and generating input values and velocities with some prescribed bounds defined by the user. Based on the Lyapunov-theory, asymptotic stability of the origin of the closed-loop error dynamics is attained, which implies that the position regulation objective is achieved while keeping the input and velocity values within prescribed bounds defined by the user. The new control scheme is assessed through numerical simulations, which corroborate the new saturated controller's feasibility.

Robust Tracking Control of the Euler-Lagrange System Based on Barrier Lyapunov Function and Self-Structuring Neural Networks

This article studies the robust tracking control problems of Euler–Lagrange (EL) systems with uncertainties. To enhance the robustness of the control systems, an asymmetric tan-type barrier Lyapunov function (ATBLF) is used to dynamic constraint position tracking errors. To deal with the problems of the system uncertainties, the self-structuring neural network (SSNN) is developed to estimate the unknown dynamics model and avoid the calculation burden. The robust compensator is designed to estimate and compensate neural network (NN) approximation errors and unknown disturbances. In addition, a relative threshold event-triggered strategy is introduced, which greatly saves communication resources. Under the proposed robust control scheme, tracking behavior can be implemented with disturbance and unknown dynamics of the EL systems. All signals in the closed-loop system are proved to be bounded by stability analysis, and the tracking error can converge to the neighborhood near the origin. The numerical simulation results show the effectiveness and the validity of the proposed robust control scheme.

Adaptive chattering-free terminal sliding-mode control for full-order nonlinear system with unknown disturbances and model uncertainties

This study investigates an adaptive chattering-free sliding-mode control method for n-order nonlinear systems with unknown external disturbances and uncertain models. The proposed method takes the advantage of finite-time fast convergence to avoid singularity problem and ensure its robustness against system uncertainty and unknown disturbance. To achieve fast convergence from any initial condition to system origin, a full-order terminal sliding-mode controller containing differential terms is proposed based on the property of n-order nonlinear systems. Then the continuous and smooth actual control law is obtained by integrating the differential control law containing the discontinuous sign function to realize chattering free. Meanwhile, instead of evaluating the fixed upper bound of system uncertainty and interference in practical implementations, an adaptive method is utilized for its unknown upper bound estimation. The convergence of the adaptive terminal sliding-mode controller in finite time is verified based on Lyapunov stability theory. Finally, two simulation results demonstrate the effectiveness of the proposed control method.